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PROBLEMS ABOUT WAR 



FOR CLASSES IN ARITHMETIC 



BY 

DAVID EUGENE SMITH, Ph.D., LL.D. 



WITH AN INTRODUCTION BY 

PAUL MONROE, Ph.D., LL.D. 

CHAIRMAN OF THE COMMITTEE ON TEXT BOOKS 



NEW YORK 
1916 



IHw. of EibliosrmJ&jp 
Lib. of Congress 



REQUESTS FOR ADDITIONAL 

COPIES OR FOR FURTHER INFORMATION 

SHOULD BE ADDRESSED TO 

DIVISION OF INTERCOURSE AND EDUCATION 

CARNEGIE ENDOWMENT FOR INTERNATIONAL PEACE 

407 WEST 117th STREET 

NEW YORK CITY 



DEC 7 1915 



<\ 



^ 



INTRODUCTION 



This pamphlet is issued with two purposes. The first is that 
of presenting to school children some of the facts regarding the 
price that is paid for the militant activities of nations. The 
second is that of enlisting their cooperation and that of teach- 
ers of mathematics in the preparation of similar problems 
through the study of facts. The larger pamphlet which is pro- 
duced by these competitive efforts will in time be placed at 
the service of teachers of mathematics or of those who prepare 
texts in arithmetic. It is not desired to give the children of 
our schools any unfair bias, but simply to present to them some 
facts to the knowledge of which they are entitled. It is hoped 
that from a familiarity with such facts presented in connection 
with the various subjects of study, a broader patriotism and 
higher ideals may result. It should be noted by the teacher that 
the formulation of problems from phenomena of our present 
environment and the use of mathematical processes to solve 
actual problems of our social life, is in accordance with the 
soundest educational principles. 

In order to elicit the interest and cooperation of pupils and 
teachers, the following prizes are offered by the Carnegie 
Endowment for International Peace : 

1. For each of the five best sets of ten problems prepared 
by the pupils of a class in the fifth grade in any public school in 
the United States, ten dollars, the money to be devoted by the 
class to the purchase of pictures for the school room. 

2. The same for the sixth grade. 

3. The same for the seventh grade. 

4. The same for the eighth grade. 

5. For each of the five best sets of fifteen problems on the 
wastefulness of war, prepared by any teacher of mathematics 
in the United States and submitted on or before April 30, 1916, 
the sum of twenty-five dollars will be paid; for each of the 
five next best sets, fifteen dollars ; and for each of the five 
third best sets, ten dollars, the money to become the property 
of the teacher. 

6. The Carnegie Endowment for International Peace shall 
cause the problems to be examined by a committee, and shall be 
the sole judge in the rendering of the decision. An effort will 
be made to announce the decision by June 30th, 1916. All 
problems submitted are to be the property of the Endowment 
for further publication and distribution. 

Paul Monroe. 



PROBLEMS ABOUT WAR 

FOR CLASSES IN ARITHMETIC 

By DAVID EUGENE SMITH 



General Object of these Problems. — The general object of 
these problems is apparent. Briefly stated, they are designed 
to lay before young people in the elementary schools, at the 
most impressionable age, the fact of the wastefulness of war. 
The questions are so framed as to emphasize this point at 
various stages in the study of arithmetic, and to do it in such a 
way as to give the pupil not only some valuable work in com- 
putation but some facts which will influence his later thoughts 
and actions on the question of war. 

On the Nature of a Good Problem. — In order to be a good 
problem in arithmetic, a question must involve the kind of 
computation which the average citizen needs to know, which 
principle excludes such a topic as cube root ; it must ask for 
a result which the average citizen might naturally wish to find, 
which principle excludes the finding of the time in which a 
given sum will yield a given interest at a given rate ; it must 
be interesting, or easily capable of being made interesting to 
a pupil, which excludes problems about the population of a 
place like Mukden ; and it must be stated in language which 
is fairly familiar to the class, which, in the early grades, ex- 
cludes problems about proteids. For example, the following 
is a type of a bad problem : "The cost to France of the Franco- 
Prussian war of 1870, in francs, is the positive root of the 
quadratic equation x 2 — 17,999,999,998jr —36,000,000,000=0. 
Find the cost." Such a problem is ridiculous. No one would 
ever find the cost in any such way, and the mere statement of 
the question would bring reproach upon the subject of algebra. 
Equally bad would be a problem framed on such a plan as 
this: "In 1913 the amount paid by England for war pur- 
poses plus the amount paid by France was so much, while five 
times the amount paid by England minus twice the amount 
paid by France was so much. Find the amount paid by each." 
Now it would be evident to any pupil that the one who framed 
a question as absurd as this must have known the answers in 
advance, and that the only purpose of the question would be 
to puzzle the learner, and so the problem would have substan- 
tially no value. 



It is for such reasons as these that the problems relating to 
the wastefulness of war must, in the main, be those of simple 
arithmetic. We use algebra, trigonometry, the calculus, de- 
scriptive geometry, geodesy, and the like, in military and naval 
affairs, but we do not use them for the purpose which we have 
in mind in this series of problems, and any attempt to use them 
here would bring reproach upon the whole movement. 

Necessity for Fairness. — No effort of this kind can be suc- 
cessful or should be successful if it is characterized by a spirit 
of unfairness. If pupils believe that the truth is not being told 
to them, the lesson sought to be inculcated will all be lost. Al- 
though the data of these problems are taken from the best 
authorities, and are supposed to be correct, it must be under- 
stood that they are presented for the avowed purpose of show- 
ing the wastefulness of war, not only in money but in life and 
in whatever admits of numerical measurement. This is done, 
however, with entire fairness, and it is believed that the con- 
clusions which a pupil is led to draw from the problems are 
correct. On the other hand, it should be distinctly admitted 
that there is an argument on the other side of the question as 
to the financial loss through war. A nation economizes in war 
times. At the close of 1914 the Bank of England had nearly 
$900,000,000 on deposit, against an average of about $300,- 
000,000 before the war. If the European war costs $1,000,- 
000,000 a month, as estimated, and the population of the war- 
ring countries is 450,000,000, the cost is about $2.10 per month 
per person, and Europe can economize more than that and not 
seriously feel the financial sacrifice. Indeed, it may learn 
valuable lessons of economy by so doing. These arguments 
are mentioned in the spirit of fairness, and not because it is 
believed to be a good thing to put money into powder, or for 
Europe to be forced to economize $2.10 per month, per person. 
Similarly, there is some argument for military training on the 
score of health and discipline, of discontent with a life of in- 
dulgence, and so on, all of which must be recognized, although 
insignificant in comparison with the tremendous loss and waste 
which a study of military expenses shows. On the other hand, 
there are many losses caused by the present European war 
that we have no means of measuring and cannot include in 
sets of problems. A factory may have a hundred employees, 
all but twenty being above the age limit of military service; 
but these twenty may include all who are trained to do a special 
line of work in the factory, and their absence may result in 
closing the concern and throwing all the others out of employ- 
ment. In one locality the flour mills may thus be shut down ; 
in another, the mines ; in another the machine shops, and so on, 
the damage arising from the absence of a few men being entire- 
ly out of proportion to the number of individuals who are 
called to arms from the particular locality. 



It is also necessary to admit the reasonableness of adequate 
preparation for national defence, but it is believed that a study 
of problems like these will bring the next generation to weigh 
more carefully the question of the proper use of the money 
needed for such a purpose, and to consider whether the world 
is not by this time old enough to settle its disputes by a resort 
to arbitration instead of brute force. 

Special Purpose of these Problems. — These problems are 
sent to thousands of teachers and textbook writers through- 
out the United States with a special purpose. It is hoped that 
teachers will use them in their classes, always with the due 
moderation that will maintain the pupil's interest and cause 
him to think out the real lesson of these statistics. It is also 
hoped that textbook writers will consider the advisability of 
using this or similar material, always within reason, perhaps 
to the extent of only a problem or two, and that school author- 
ities will ask their teachers to frame occasional questions of 
this nature and to encourage their pupils to do likewise. It will 
be seen that the problems here given are not controversial in 
the slightest degree ; they have nothing to do with the merits 
of the present war or of any past war ; they do not enter into 
the questions of national defense, of pensions, or of adequate 
equipment of our army and navy ; their sole purpose is the one 
above stated — to cause the pupils to think of their responsibility 
in assisting to create a world-sentiment in favor of a wiser use 
of money than in mere armaments. 



THE PROBLEMS 

The Cost of War 
Problems Involving the Four Operations With Integers. 

1. In the war of 1870 France lost in killed, wounded, and 
prisoners 723,500 officers and men in eight months, and Ger- 
many lost 129,647. Find the total loss of both countries, and 
the average loss per month and per day. 

In all such cases take 30 da. to the month. 

2. In the great wars from 1790 to 1913 there were 5,498,- 
097 men killed. In the United States it is estimated that the 
average value of each life (man, woman, or child), based upon 
the value of the annual products of the country, is $2900. 
Taking the value of these men, all of them much above the 
average in health and strength, although living where human 
life was not economically so valuable, as $2900, what was the 
financial cost to the world in the loss of all these lives? 

3. If in the great war of 1914-1915 there are 2,500,000 
men killed, what is the financial loss of these human lives, on 
the basis of the average given in Ex. 2? 

4. Valuing a human life economically at $5000, what 
would be the loss by the conditions of Ex. 3? 

5. It is estimated that 21,200,000 were engaged in the 
great war of 1914-1915. Suppose each man could produce $2 
a day, on the average, if he remained at home and worked, 
what is the loss per day in production by taking these men 
away from work? 

G. In Ex. 5, what is the loss per month? What is the 
loss per year? 

7. The mere cost of transporting the armies in the great 
war of 1914-1915 was $2,100,000 a day. How many poor 
people could be helped each day with such an amount, allowing 
50c. a day to each person ? 

8. In this war it costs $1,000,000 a day to feed the horses 
used in the armies. How much does this amount to in a year? 
At $500 each, to how many boys and girls could be given a year 
in college for this amount paid for horse feed ? 



Guns and Colleges 
Problems Involving Multiplication and Division. 

1. Five superdreadnoughts of the Queen Elizabeth type 
are put in commission by Great Britain in 1915. The powder 
used in firing a single shot from one of the eight 15-inch guns 
costs $750. How much will it cost, for powder alone, to fire 
one round of the eight guns on a single ship? How much will 
it cost for the five ships? 

2. The average annual tuition for a student in a certain 
college or university is $150. The mere powder required for 
a single round of shots from the five superdreadnoughts in 
Ex. 1 would pay the tuition of how many students for a year? 
Answer to the nearest unit in all such cases. 

3. The cost of each of the 15-inch guns mentioned in Ex. 1 
is $80,000. How much did the guns for the five superdread- 
noughts cost? 

4. A student's necessary living expenses in college aver- 
ages $250 a year. The cost of the large guns for the five ships 
mentioned in Exs. 1 and 3 would pay the living expenses of 
how many college students for a year? 

5. If all the five ships mentioned in Ex. 1 should fire 
100 rounds during the year 1915, the mere powder consumed 
would cost how much ? 

6. The total annual income of a certain state university 
is $310,000. The powder mentioned in Ex. 5 would provide 
the annual income of this university for how many years? 

7. A first-class battleship, fully equipped, will cost next 
year about $15,000,000. Such an amount would build and 
equip trade-schools, at $75,000 each, in how many cities? 

8. The sum mentioned in Ex. 7, as the cost of a battleship, 
would send how many boys or girls through a business college, 
allowing $1,500 to each student? 

9. It is proposed to build a series of forts and equip them 
with modern guns to defend one of our seaports. The expense 
is estimated at $2,500,000. Such a sum would pay the expenses 
of how many boys next year in a good school of technology, 
allowing $500 for each boy ? 

Such a problem is not intended to show that adequate defence 
is not a wise precaution. It is simply intended to call attention to 
the amount of money that is being expended because the world will 
not agree to settle disputes in a rational manner. 

10. To fire some of the guns in modern ships costs $1,200 
for each shot, including all charges. If such a gun is fired 
once in three minutes for an hour a day on each of the seven 
days of a week, the expense is how much? This sum would 
pay your expenses in college, at $500 a year, for four years, 
and the expenses of how many of your friends at the same 
rate? 

10 



War Expenses and Our Pleasures 
Problems Involving Long Division. 

1. There are 300,000 Boy Scouts in America, and $30 on 
an average would give each of them a camping trip and a scout 
suit this year. We spent on our War Department $173,522,- 
804 last year. This amount would pay these expenses of the 
Boy Scouts for how many years? 

In all such cases answer to the nearest year or other unit. 

2. Most boys would like to go to a ball game every week. 
If a boy went to a game every week for a season of twenty 
weeks, and took a 50c. seat, how much would it cost for the 
season? The amount which we spent on our navy last year, 
$139,682,186, would pay for tickets for how many boys? 

3. A Camp-Fire Girl can, for $35, buy her suit and pay 
for a camping trip in the summer. The $173,522,804 which our 
Government spent last year on the War Department would 
pay these expenses for how many girls? 

4. A good tennis racket can be bought for $1.50. The 
battleship Vermont cost $7,563,963. This amount would buy 
rackets for how many boys and girls? 

5. A baseball suit can be bought for $4.50. The battle- 
ship Virginia cost $6,703,614. This amount would buy suits 
for how many boys? 

6. A ticket to some good entertainment costs on the aver- 
age 25c. The battleship South Carolina cost $5,097,355. This 
amount would buy tickets for how many boys and girls? 

7. A good bicycle can be bought for $25. The battleship 
Oregon cost $6,575,032. This amount would buy bicycles for 
how many boys and girls ? 

8. Before the great war began, Europe owed $27,000,- 
000,000 for old war debts. If we can imagine such a sum 
divided equally among the 90,000,000 families of Europe, and 
devoted to pleasure, how much would be allowed to each 
family? 

9. During the year preceding the great war, the five great 
European powers spent $898,921,000 on their armies. At 10c. 
per ticket, how many tickets to some good moving-picture plays 
would such an amount buy for each of the 450,000,000 people 
in these countries ? Answer to the nearest unit. 

10. In the year mentioned in Ex. 9, the same powers spent 
$619,511,000 on their navies. Such an amount would buy how 
many tickets per person as stated in Ex. 9 ? 

It is hoped that such examples, relating to the immediate 
interests of the pupils, may furnish means for giving them 
some idea of the vastness of expenditure for armaments. It is 
not intended to suggest that the money spent for war would 
otherwise be spent for pleasure, but to offer familiar standards 
of measure to allow our youth to appreciate the size of num- 
bers represented by these "endless caravans of figures." 

11 



Battleships and Schools 
Problems Involving Long Division. 

1. The battleship Alabama cost $4,665,820. In 1913 the 
total receipts of Alabama for higher education amounted to 
$533,659. The cost of this single battleship would have kept 
Alabama in funds for her colleges, universities, and schools of 
technology for how many years ? Answer to the nearest year. 

2. The battleship Arizona is estimated to cost $7,425,500. 
In 1913 the total amount expended for common schools by 
the state of Arizona was $1,321,631. The cost of this single 
battleship would have paid for all the common schools of 
Arizona for how many years ? Answer to the nearest year. 

3. The battleship Arkansas cost $4,675,000. The total 
value of buildings for colleges, universities, and technological 
schools in Arkansas (1913) is $654,500. The cost of this single 
battleship would pay for how many times as many such build- 
ings for this state? 

4. The battleship Connecticut cost $7,911,175. It is esti- 
mated that the average cost of education of a pupil in the 
common schools of Connecticut is $39.92 per year. The cost 
q$ this single battleship would pay for the education of how 
many pupils for a year? It would pay for the education of 
how many pupils for ten years ? Answer to the nearest unit. 

5. The battleship Delaware cost $5,705,757. This is 
how many times the total value ($1,600,000) of all the public 
property used for common school purposes in Delaware? 
Answer to the nearest unit. 

6. The battleship Florida cost $6,400,000. In 1912 
Florida received for permanent endowments for her univer- 
sities, colleges, and technological schools $1000. It would take 
the endowments for how many years, at this rate, to pay for 
this one battleship? 

7. The battleship Wyoming cost $4,450,000. The total in- 
come of the University of Wyoming in a recent year was 
$243,639. The cost of this single battleship would pay this 
total income for how many years ? Answer to the nearest unit. 

8. The battleship Vermont cost $7,563,963. It is estimated 
that the average cost of education of a pupil in the common 
schools of Vermont is $34.80 per year. The cost of this single 
battleship would pay for the education of how many pupils for 
i year? It would pay for the education of how many pupils 
for the eight years of the elementary school? Answer to the 
nearest unit. 

We have a number of battleships which we have named after 
our states. Such ships are necessarily expensive, and we feel 
that this expense is justified because of the protection we re- 
ceive. If it were not for wars we might use this money to 
better purpose, and the object of these problems is to compare the 
expenditure for ships with the expenditure for schools. 

12 



The Financial Cost of War 
Problems Involving Decimal Fractions 

1. The Franco-German war of 1870 lasted eight months 
and cost France, in expenses, indemnity paid to Germany and 
loss of territory, 18,000,000,000 fr. At 19.3c. to the franc, 
how many dollars does this represent ? How many dollars 
for each month of the war ? How many dollars a day ? 

2. The war mentioned in Ex. 1 cost Germany 2,111,000,- 
000 marks. At 23.8c. to the mark, how many dollars does 
this represent? How many dollars a month? How many 
dollars a day? 

3. The South African war of 1899-1902 cost Great 
Britain £211,156,000. At $4,866 to the pound, how many dol- 
lars does this represent? 

4. To fire a single shot from each of the big 15-inch guns 
of England's superdreadnought the Queen Elizabeth costs 
£200, and each of the eight big guns can fire three shots a 
minute. Suppose all eight guns were fired for a single minute 
as rapidly as possible, and that we take the value of the pound 
as stated in Ex. 3, what would be the financial cost? At $600 a 
year, how many young men or women could be kept in college 
next year for the money spent in thus firing these guns for 
ten minutes? 

5. If Great Britain had five superdreadnoughts of the type 
mentioned in Ex. 4 firing only their 15-inch guns for a single 
hour, the cost would pay one year's tuition at $150 of how 
many students in college? 

It must, be understood that these ships do not carry enough 
ammunition for such continuous firing. The figures are, how- 
ever, approximately correct. 

6. The Balkan. war of 1912-1913 cost Greece 606,250,000 
drachmas. A drachma is a Greek coin worth 19.3c. in our 
money. Find in our money the financial burden which this war 
placed upon Greece. 

7. The war mentioned in Ex. 6 cost Serbia 1,212,500,000 
dinars. A dinar is a Serbian coin worth 19.3c. in our money. 
Find in our money the amount which Serbia was compelled to 
pay for the war. 

8. The war mentioned in Ex. 6 cost Turkey 8,800,000,000 
piastres. A piastre is a Turkish coin worth 4.4c. in our money. 
Find in our money the amount which Turkey paid for her ex- 
penses in the war. 

9. In the year preceding the great war Russia spent 
617,000,000 rubles on her army. A ruble is a Russian coin 
worth 51.5c. in our money. Find in our money the amount 
which Russia spent on her army in that year. 

13 



War's Subsequent Financial Burdens 

Problems Involving Percentage. 

1. In 1866 we were paying $15,000,000 a year in pensions. 
In 1881 we were paying $56,000,000. What was the per cent 
of increase? 

2. In 1890 we were paying $86,000,000. What was the 
per cent of increase over 1866? over 1881? 

3. In 1913 we were paying $177,000,000. What was the 
per cent of increase over 1866? What was the per cent of in- 
crease over 1881 ? What was the per cent of increase over 
1890? 

4. In 1914 it cost our government $2,000,000 simply to 
pay its pensions and keep up the Pension Bureau. The amount 
paid in pensions in that year was $172,400,000. What per 
cent of the total amount of pensions and expenses, to the 
nearest tenth per cent was used for expenses ? 

5. Up to June 30, 1914, our government had paid as pen- 
sions the following amounts : war of the Revolution, $70,- 
000,000; war of 1812, $46,000,000; Indian wars, $13,000,- 
000; Mexican war, $49,000,000; Civil war, $4,458,000,000; 
Spanish war and Philippine insurrections, $46,000,000 ; other 
items, $49,000,000. Find the total amount paid for pensions, 
and find what per cent of this, to the nearest tenth, went for the 
civil war. 

6. The annual expenditures of our government, exclusive 
of the post office, which is practically self-supporting, are about 
$750,000,000. Of this amount $174,000,000 goes for military 
pensions. Our pensions are what per cent of our total ex- 
penses ? 

7. Referring to Ex. 6, we pay $450,000,000 a year for 
our army, our navy, and our pensions, — all war expenses while 
we are at peace with all nations. What per cent of our total 
expenses go for these purposes? 

8. In 1800 our country paid $64,131 for pensions. In 
1914 we paid $173,092,065. The amount paid in 1800 was what 
per cent of the amount paid in 1914? 

9. In 1914 we had 785,239 persons in the United States 
drawing war pensions. Taking our population as 98,646,491 
in that year, what per cent of our population was on the pen- 
sion roll? Answer to the nearest tenth per cent. 

After a war closes it is the laudable custom in most countries 
to pay pensions to those soldiers who were disabled while in 
service. Our nation is more liberal than others in this respect. 
The above problems are based upon our pension system 
and are intended to show one of the financial burdens of war, 
and not to touch in any way upon the merits of the svstem. 
Indeed, it is the duty of the: schools to encourage the legitimate 
recognition of the services of those who have fought for the 
country. 

14 



The Financial War Problems of Nations 
Problems Involving Percentage. 

1. At the outbreak of the Russo-Japanese war of 1904-5, 
the national debt of Japan was 600,000,000 yen. After the war 
was over, although Japan was victorious, the national debt was 
2,260,000,000 yen. By what per cent did the war increase 
the national debt? 

It should be observed that it is not necessary to know the value 
of the yen in our money. If it is desired to translate the above 
figures into dollars, it may be stated that a yen is approximately 
equal to 50c. (actually 49.8c.) of our money. 

2. At the beginning of the war mentioned in Ex. 1, the 
national debt of Russia was 6,630,000,000 rubles, and after the 
war expenses had been met it was 8,836,000,000 rubles. By 
what per cent did the war increase the national debt? 

Here again, the value of the ruble need not be known in 
order to solve the problem. It is approximately equal to 50c 
(actually 51.5c.) of our money. By Exs. 1 and 2 we see that 
the victorious nation may suffer financially more than the un- 
successful one. 

3. The Balkan wars of 1912-1913 cost $2,100,000,000. 
The population of Bulgaria is 4,755,000 ; of Roumania, 7,520,- 
000 ; of Serbia, 4,600,000 ; of Albania, 825,000 ; of Montenegro, 
520,000. Find the cost per capita for these Balkan states. 

Of course other states were involved, but the problem is 
intended to show the great financial cost in comparison with the 
population of the countries chiefly concerned. 

4. In particular, the wars referred to in Ex. 3 cost Bul- 
garia $436,500,000. Find the per capita cost for that country. 

5. Comparing Exs. 3 and 4, the per capita cost for Bul- 
garia was what per cent of the per capita cost for all the Balkan 
states? 

6. One of the most expensive wars of the world was our 
own civil war of 1861-1865. The cost is estimated at $5,000,- 
000,000, while the cost of our war with Spain is estimated at 
23.3% as much. How much did these two wars cost? 

7. The Transvaal War of 1900-1901 is estimated to have 
cost £200,020,000, and the war between Italy and Turkey, in 
1911, to have cost 70% as much. At $4,866 to the pound, find 
the cost of each of these wars in our money. 

8. Before the great war of 1914-1915, the national debt 
of the United Kingdom (Great Britain and Ireland), largely 
due to war, was $3,485,818,000, and the entire wealth of the 
country was estimated at $85,000,000,000. The debt was what 
per cent of the total wealth ? Answer here and in Ex. 9 to the 
nearest tenth per cent. 

9. As in Ex. 8, the national debt of France was $6,346,- 
129,000, also largely due to war, and the entire wealth of the 
country was estimated at $50,000,000,000. The debt was what 
per cent of the total wealth ? 

is 



The Human Sacrifice of War 
Problems Involving Percentage. 

1. In the war between France and England from 1793 to 
1815, out of 3,000,000 men engaged 1,900,000 were killed. 
Find the per cent of deaths. 

2. In the European wars of 1854-1856, 1,460,500 men 
were engaged and 41.7% were killed. Find, to the nearest 
thousand, the number killed. 

3. In the Civil War of the United States, 404,400 men 
were killed. This was 17.8% of the total number engaged. 
Find, to the nearest thousand, the number of men engaged. 

4. In the Franco-German war of 1870-1871 there were 
1,713,000 men engaged, and 311,000 were killed. Find the 
per cent of deaths. 

5. In the war between Russia and Turkey in 1876-1877, 
there were 1,500,000 men engaged, of whom 12% were killed. 
How many were killed? 

6. In the Russo-Japanese war of 1904-1905 there were 
555,900 men killed, which was 22.2% of the number engaged. 
Find, to the nearest thousand, the number of men engaged. 

7. In the great wars from 1790 to 1913 there were 18,- 
552,200 men engaged, of whom 5,498,097 lost their lives. Find 
to the nearest tenth per cent the per cent of those who were 
killed. 

8. Taking a general average, let us suppose that each man 
killed, as stated in Ex. 7, was the father of two children. How 
many children were left fatherless by these wars ? 

9. Instead of making the supposition of Ex. 8, let us sup- 
pose that only 66^% of the men were married. How many 
women were made widows by these wars? 

10. In the Balkan wars of 1912-1913 there were 1,230,000 
men engaged and 350,000 of these lost their lives, whereas in 
the Russo-Japanese war of 1904-1905 there were 2,500,000 men 
engaged, of whom 555,900 lost their lives. In which war was 
the per cent of loss the greater? State the per cent of loss in 
each case. 

11. It is estimated that in the present great war there are 
21,200,000 men engaged. If the per cent of loss of life should 
be the same as that in the Balkan wars (see Ex. 10) what 
number of men would be killed. 

It should be stated that examples like Exs. 3 and 6 are not to 
be commended. We seldom have to find the number of men 
engaged, for this number is usually known. It is also open 
to question whether the attempt to draw a moral by such 
hypothetical cases as Exs. 8 and 9 is warranted. If the facts 
were really known the problems would be justified. 

16 



Cost of Saving and of Destroying Human Life 

Problems Involving a Knowledge of Simple Interest. 

1. Pittsburg recently spent $7,000,000 on purifying its 
water supply. It is estimated that 300 lives a year will be saved 
by having pure water, and that these lives are worth, on an 
average, $5000 to the city and country. How much is the 
financial saving of human life ? 

2. If Pittsburg borrowed the $7,000,000 at ± l A%, how 
much would the average charge be per year ? 

3. The expenditures for 2,000,000 shrapnel shells at $18 
each which a certain European government placed in one 
order in 1915, was how many times the annual interest charge 
found in Ex. 2 ? It was how many times the entire charge of 
the purifying plant mentioned in Ex. 1 ? Answer to the near- 
est tenth in each case. 

4. The death rate of infants in a certain English town was 
recently reduced one-third at the average expense of $20 per 
child saved. The mere cost of ten shrapnel shells at the rate 
mentioned in Ex. 3 would pay for the saving of how many 
children's lives at this rate? 

5. At 5% the interest on the cost of a single battleship like 
the Pennsylvania ($13,000,000) would save how many 
children's lives at the figures given in Ex. 4 ? 

6. In Germany it costs on the average 2310 marks to rear 
a child from birth to the age of 20 years. At 23.8c. to the 
mark, how much is this in our money? At 6% the interest 
for 20 years on a battleship costing $9,500,000 would pay for 
the rearing of how many children in that period? 

7. The United States government pays for the promotion 
of public health $4,425,188 in the year ending June 30, 1916. 
At 2^%, a fair rate of interest for the government, this is how 
much less than the mere interest on the $459,071,803 that we 
spend this year for war purposes ? 

8. The battleship South Carolina cost $5,097,355. Last 
year the state of South Carolina appropriated $42,220 for pub- 
lic health. One year's interest on the cost of the battleship, at 
5%, would pay the amount appropriated for public health for 
how many years? 

9. The mere hull and machinery of the battleship Okla- 
homa cost $5,926,000. Last year the state of Oklahoma appro- 
priated $32,700 for public health. The interest on the cost of 
the battleship, at 5%, would allow this appropriation to be in- 
creased how much? 

10. The battleship Kansas cost $7,565,620. Last year the 
state of Kansas appropriated $30,500 for public health. This 
represents, to the nearest tenth per cent, the interest on the cost 
of the battleship at what rate? 

17 



Battleships and Teachers 
Problems Involving a Knowledge of Simple Interest. 

1. The battleship Georgia cost $6,543,531. The average 
monthly salary of a teacher in Georgia is $45.54. The mere 
interest on the cost of this battleship at 6% would pay the 
salary of a teacher for how many years of 9 months each ? 

2. The battleship Illinois cost $4,621,408. The average 
monthly salary of a teacher in Illinois is $73.05. The interest 
on the cost of this battleship at 6% would pay the salaries of 
how many teachers for a month? 

3. The battleship Indiana cost $5,983,371. The average 
monthly salary of a teacher in Indiana is $66.01. The interest 
on the cost of this battleship at 5% would pay the salaries of 
how many teachers for the year in which the interest is paid? 

4. The battleship Iowa cost $5,871,206. How much would 
the simple interest on this sum amount to in the 15 yr. of the 
life of the ship? The average monthly salary of a teacher 
in Iowa is $51.67. This interest, plus the cost of the ship, which 
is then out of date, would pay the salaries of how many teach- 
ers 9 mo. in each year for the 15 yr. ? 

5. The battleship Kansas cost $7,565,620. In 1913 the 
state of Kansas received from the United States government 
$80,000 for higher education. The interest on the cost of the 
battleship, at 6%, would have allowed this amount to be how 
many times as great? 

6. The battleship Kentucky cost $4,998,119. In 1913 the 
state of Kentucky received from the United States govern- 
ment $72,750 for higher education. The interest for a single 
year on the cost of the battleship, at 5%, would have paid this 
sum for how many years ? 

7. The battleship Louisiana cost $7,425,613. The average 
monthly salary of a teacher in Louisiana is $55.51. The in- 
terest on the cost of this battleship for a single month, at 6% 
would pay the salaries of how many teachers? 

8. The battleship Maine cost $5,381,903. The average 
annual salary of a teacher in the common schools of Maine is 
$450. The interest on the cost of this battleship, at 6%, would 
pay the salaries of how many teachers ? 

9. The battleship Massachusetts, built in 1891, cost 
$6,017,117, and is now obsolete. Suppose, instead of putting 
the money into this battleship, it had been placed at simple in- 
terest at 5%. The money would still be unspent, and it would 
have accumulated how much interest from the time the ship 
was built to the year 1915? 

18 



Cost of Saving Life and Cost of Destroying Life 

Problems Involving Simple Interest. 

1. The battleship New York cost, for hull and machinery 
alone, $6,400,000. This year New York State spends 
$257,940 on the department of health. How does the mere 
interest on this part of the total cost of the battleship, at 
4j4%, compare with the amount devoted to public health? 

This is the regular appropriation of New York for 1914-1915, 
and similarly in the following examples. 

2. The battleship Illinois cost $4,621,408. This year Illi- 
nois spends $112,115 on the department of health. If, instead 
of putting this amount into this battleship, which is now 
nearly obsolete, the same amount had been put at interest 
at 4^2%, how long could this department of health have 
been maintained at its present expense? What annual income 
would result indefinitely at this rate of interest? 

It should be stated in fairness to the pupils that Illinois 
did not pay for this ship directly, and that if the money had 
not been put into building the ship it would not have been given 
to Illinois for purposes of public health. On the other hand, 
the $4,621,408 represents but a fraction of the total cost of the 
ship since it was built (1897), and the ship is nearly worthless 
at present. Similar considerations apply to many of these ex- 
amples. All that these problems seek to show is that it is a 
pity that the world cannot find a better plan for ensuring peace 
than by spending these vast amounts. 

3. The hull and machinery alone of the battleship Michi- 
gan cost $3,585,000. This year Michigan spends $39,000 on the 
department of health. At 4% the interest on this partial 
cost of the battleship would increase the appropriation for 
health by how much, besides continuing it indefinitely with no 
further expense? 

4. The battleship Texas, with full equipment, cost about 
$12,500,000. This year Texas spends $48,200 on the depart- 
ment of health. The interest on the cost of the battleship 
would enable Texas to spend how many times this amount 
for public health forever? 

5. The United States Life-Saving Service cost our Gov- 
ernment $2,309,317 last year, and cared for 29,000 ship- 
wrecked persons. In the same year we spent $173,522,804 on 
our army, $139,682,186 on our navy, and $173,440,231 on 
pensions, all these being expenses due to war or fear of war. 
The amount devoted to our Life-Saving Service was how 
much less than the interest on the sum of these war expenses 
at 2%, which is about the rate that our Government has to 
pay? 

Teachers should encourage the pupils to find the amount 
epent locally, where they live, for the purposes of public health, 
and to make up problems similar to Ex. 5, based on this in- 
to rmati on. 

19 



The Cost of War 
Problems Involving Stocks and Bonds. 

1. Countries borrow money for public buildings and other 
permanent improvements, issuing bonds and usually paying a 
certain amount from year to year. Before the great war the 
per capita debt of Great Britain was $72 ; of Germany, $18 ; of 
France, $166; of Belgium, $97; of Austria-Hungary, $48; of 
Russia, $21 ; and of Serbia, $44. On January 1, 1915, this 
had increased so that the debt of Great Britain was $106 per 
capita; of Germany, $57; of France, $212; of Belgium, $114; 
of Austria-Hungary, $83 ; of Russia, $36 ; and of Serbia, $88. 
Find the per cent, of increase for each country for the first 
five months of the war (August to January). 

By per capita debt is meant the average which each man, 
woman, and child in a country would have to pay to cancel 
the whole debt. 

2. To carry on the first five months of the great war, 
Great Britain had to borrow $1,560,000,000; France, 
$1,815,000,000; Germany, $2,600,000,000; Belgium, $130,- 
000,000 ; Austria-Hungary, $1,815,000,000 ; Russia , $2,600,- 
000,000 ; and Serbia, $130,000,000. How much was borrowed 
by these seven countries? How much did this average per 
month ? 

3. The daily cost of the great war is estimated at $50,- 
000,000. At this rate, how much will it amount to in the year 
from August 2, 1914 to August 2, 1915? 

4. If the countries borrow the money mentioned in Ex. 3, 
and pay on an average 5% interest on their indebtedness, the 
interest alone will amount to how much per year? 

5. Largely as a result of wars or appropriations for war, 
England had, before the war began, a debt of $3,305,000,000 ; 
Germany, $1,200,000,000; France, $6,575,000,000; Belgium. 
$740,000,000; Austria-Hungary, $2,450,000,000; Russia, $4,- 
450,000,000; and Serbia, $130,000,000. From these figures 
and those in Ex. 2, compute the debts of these countries after 
five months of war. 

6. Before the war, Belgium's 3% bonds were quoted at 
96, and Germany's 3% bonds at 82. What was the actual rate 
of interest which each of these countries, the former with no 
well-trained army, and the latter with a remarkable military 
organization, have to pay ? 

7. Before the war, Norway's Z l / 2 % bonds were quoted at 
102, and Russia's at 81. What was the actual rate of interest 
which each of these countries, the former giving little attention 
to war, and the latter well equipped, had to pay t 

The object of Exs. 6 and 7 is to show that the credit of a 
country in the money markets of the world is not proportional 
to the attention paid to armaments. 

20 



Losses Occasioned by Rumors of War 
Problems Involving a Knowledge of Stocks and Bonds. 

1. Between July 22 and July 30, 1914, the prices of 
British 2^% bonds declined from 75£ to 70. What was the 
actual rate of interest on the money borrowed at each of 
these quotations? If Great Britain needed to borrow more 
money, which she and most European countries did, would 
she be actually paying more interest, or less interest? 

The great European War began in August, 1914. Rumors 
of war had been heard some days before war was actually de- 
clared. Between July 22 and July 30 all European and Ameri- 
can stock exchanges felt the serious effects of these rumors. 
The examples on this page relate to this period, and to govern- 
ment bonds or their equivalent. 

2. French 3% bonds declined from 81 to 76£. If France 
needed to borrow more money, what interest would she 
actually have to pay at each of these quotations? 

3. German 3% bonds declined from 75 to 72. If Ger- 
many needed to borrow more money, what interest would she 
actually have to pay at each of these quotations? 

4. Austrian 4% bonds declined from 84-1 to 76^. What 
interest would Austria actually have to pay at each of these 
quotations ? 

5. Russian 5% bonds declined from 102^ to 93. What 
interest would Russia actually have to pay at each of these 
quotations ? 

6. Exs. 1-5 tell us something about the relative financial 
standings of the five great powers at the beginning and end of 
the week preceding the declaration of war. Which country 
could borrow money at the lowest rate of interest at the be- 
ginning of the eight days ? Which could borrow money at the 
lowest rate at the end of the eight days? 

7. The market value of the securities quoted on the Lon- 
don stock exchange fell, in the eight days mentioned, £600,- 
000,000. That is, the stocks and bonds quoted on that ex- 
change would sell for that much less. At $4,866 to the pound, 
what was the loss in value in these securities alone, caused by 
rumors of war? 

8. Let us try to measure the enormous sum mentioned in 
Ex. 7. Not counting leap years, but taking 365 days to each 
year, how many days in the 1915 years from the beginning of 
the Christian era? If this sum of money were apportioned 
equally among these days, each day would represent how much 
money ? 

9. Let us try to measure the sums in Exs. 7 and 8 in 
another way. How much money would each of the 2,000 work- 
ing men in one of our small cities, and his successors, have to 
earn a day for 1915 years to equal simply the losses on the 
London Stock Exchange in the eight days preceding the war? 

21 



The Financial Cost of War 
Problems involving a Knowledge'*' of Stocks and Bonds. 

1. To pay her great loss to Germany in the war of 1870, 
France first issued $150,000,000 worth of 3% bonds and sold 
them at 60.6% of their par value. What rate of interest did she 
have to pay on the money actually received? How much in- 
cerest did she pay per year on this loan? 

2. France also issued $50,000,000 worth of 6% bonds and 
sold them at 85% of their par value, and $400,000,000 worth of 
5% bonds and sold them at 82.5% of their par value. On which 
of these loans did she pay the higher rate of interest on the 
money actually received ? How much interest did she pay per 
year on each of these two loans? on the two together? 

3. To finance the South African war of 1899-1902, Great 
Britain was forced to borrow a large amount of money through 
the sale of bonds. She sold £30,000,000 worth of 2f% bonds 
at 98^, £60,000,000 worth at 94£, and £32,000,000 worth at 
93£. How much actual cash did she receive from these sales, 
how much interest did she have to pay a year, and what was 
the actual rate of interest on the cash received? 

The teacher should call attention to the fact that Great Britain 
sold her bonds first at 98 J4, then at 94*4, and finally at 93J4 
her credit decreasing as the war continued. As a matter of 
fact her bonds (Consols) were selling at 102^4 when the war 
was declared, whereas they are now (1915), largely as a result 
of war and armament charges, selling at about 70, a tremendous 
shrinkage in values. 

4. The loss occasioned by the war mentioned in Ex. 3, 
also affected railway stocks in Great Britain. Partly as a re- 
sult these stocks declined £300,000,000 in value. Compute this 
shrinkage in dollars, at 4.866 to the pound. 

5. In the Russo-Japanese war of 1904-5 Japan had to 
borrow large sums by issuing government bonds. Her credit 
declined as the war proceeded, although she was successful in 
her battles. At first (March 1904) she sold her 5% bonds for 
95 ; then (May and October, 1914) her second and third issues 
of 5% bonds for 92; then (February and May, 1905) she had 
to issue 6% bonds at 90. Find the rate of interest which she 
had to pay on the money she actually received for her bonds in 
each of these three cases. 

These did not represent all the loans, but they represent the 
money borrowed at home, and they show how even a successful 
war impairs the financial standing of a country. 

6. The world's annual armament bill in times of peace, 
that is, in the year preceding the great war of 1914, was $2,324,- 
067,000. Let us try to realize how vast a sum this is. What 
is the population of the place in which you live? If one fourth 
of these persons are wage earners, and average $2 a day, 
how much can they earn in a day? How many days would 
it take them to earn this amount ? How many years ? 

22 



The Financial Cost of War 
Problems Involving Ratio and Proportion. 

1. The South African war began Oct. 11, 1899, and on 
Oct. 20, 1899, the British ministry estimated that it would cost 
£10,000,000. It turned out that the ratio of estimated cost 
to actual cost was substantially 25 : 53. At this ratio, how 
much did the war really cost ? 

2. The Russo-Japanese war of 1904-5 cost Japan 2,030,- 
943,000 yen, a yen being equal to 50c. of our money. The 
amount charged to the national debt (that is, the amount bor- 
rowed) was to the amount paid for out of the current revenues 
(that is, the amount paid for as the war went on) as 98 : 27. 
Find the number of dollars added to Japan's national debt by 
this war in which she was successful. Find also the number 
of dollars she had to pay at once. 

3. For the year ending June 30, 1916, it is estimated that 
our country will spend for army, navy, pensions, and other 
matters relating to war, the sum of $459,071,803. Our total 
expenditures for the year are estimated as $1,090,775,134. 
Find to the nearest hundredth the ratio of our war expenses 
to our total expenditure. 

4. For the year mentioned in Ex. 3 our war estimates are, 
as stated, $459,071,803, and our estimated expenses for such 
peaceful purposes as agriculture, labor, education, foreign 
affairs and care of the Indians are $196,306,267. Find to the 
nearest hundredth the ratio of our peace expenses to our war 
expenses. 

5. The battleship Pennsylvania, launched in 1915, cost 
$13,000,000. It cost our country $211,840 to pay our Presi- 
dent and Vice-President, and to meet the expenses of the ex- 
ecutive offices of the government. The cost of this single 
battleship would pay these expenses for how many years? 

6. In the year 1914 the United States, at peace with all 
the world, with a very small army and a navy that ranked 
only third or fourth in the navies of the world, spent 
$173,894,143 for her army, $139,893,614 for her navy, and 
$173,092,065 on pensions. What was the ratio, to the nearest 
tenth, of our total war expenses to the war expenses of Ger- 
many in 1913, with the best-equipped army in the world, these 
expenses being $312,967,000? 

7. In Ex. 6, find the ratio of our war expenses to the 
war expenses of England in 1913, with the best-equipped 
navy in the world, these expenses being $351,044,000. 

8. In Ex. 6, find the ratio of our war expenses to the 
war expenses of France in 1913, with a large army and good- 
sized navy, these expenses being $259,349,000. 

Exs. 6-8 show that we spend a very large amount in pro- 
portion to the results. Part of this is undoubtedly legitimate, 
for we pay our workmen, our soldiers, and our sailors better 
than most other countries. 

23 



,L««*r OP conbbss 




eiJ 39 |-w (i 



I 



PUBLICATIONS OF THE CARNEGIE ENDOWMENT 
FOR INTERNATIONAL PEACE 



Division of Intercourse and Education. 



No. 1. Some Roads Towards Peace : A report on observa- 
tions made in China and Japan in 1912. By Dr. 
Charles W. Eliot. 

No. 2. German International Progress in 1913. By Pro- 
fessor Dr. Wilhelm Paszkowski. 

No. 3. Educational Exchange with Japan. By Dr. Hamilton 
W. Mabie. 

No. 4. Report of the International Commission to Inquire 
into the Causes and Conduct of the Balkan Wars. 

No. 5. Intellectual and Cultural Relations between the United 
States and the Other Republics of America. By 
Dr. Harry Erwin Bard. 

No. 6. Growth of Internationalism in Japan. By T. 
Miyaoka. 



Information about Year Books and about the publications 
of the Division of Economics and History and of the Division 
of International Law may be obtained by addressing the Secre- 
tary, Carnegie Endowment for International Peace, 2 Jackson 
Place, Washington, D. C. 



